





"""simple docstring"""



from itertools import product







def 						__lowercase	(  snake_case_    :    List[str]							,snake_case_    :    Dict		)  ->list[int]:



    '''simple docstring'''







    __A       :		Dict							=	sides_number
    __A       :		Optional[Any]							=	max_face_number * dice_number
    __A       :		List[Any]							=	[0] * (max_total + 1)

    __A       :		int							=	1
    __A       :		Optional[int]							=	range(__lowerCAmelCase							,max_face_number + 1		)
    for dice_numbers in product(__lowerCAmelCase							,repeat=__lowerCAmelCase		):
        __A       :		Any							=	sum(__lowerCAmelCase		)
        totals_frequencies[total] += 1

    return totals_frequencies







def 						__lowercase	(  )  ->float:



    '''simple docstring'''







    __A       :		List[Any]							=	total_frequency_distribution(
        sides_number=4							,dice_number=9		)
    __A       :		Union[str, Any]							=	total_frequency_distribution(
        sides_number=6							,dice_number=6		)

    __A       :		List[str]							=	0
    __A       :		Tuple							=	9
    __A       :		int							=	4 * 9
    __A       :		Optional[int]							=	6
    for peter_total in range(__lowerCAmelCase							,max_peter_total + 1		):
        peter_wins_count += peter_totals_frequencies[peter_total] * sum(
            colin_totals_frequencies[min_colin_total:peter_total]		)

    __A       :		Tuple							=	(4**9) * (6**6)
    __A       :		Dict							=	peter_wins_count / total_games_number

    __A       :		Optional[Any]							=	round(__lowerCAmelCase							,ndigits=7		)

    return rounded_peter_win_probability


if __name__ == "__main__":
       print(f'''{solution() = }''')





"""simple docstring"""


import os
from shutil import copyfile
from typing import List, Optional, Tuple

from ...tokenization_utils import AddedToken
from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import is_sentencepiece_available, logging


if is_sentencepiece_available():
	from .tokenization_albert import AlbertTokenizer
else:
	a				=None

a				=logging.get_logger(__name__)
a				={'vocab_file': 'spiece.model', 'tokenizer_file': 'tokenizer.json'}

a				={
    'vocab_file': {
        'albert-base-v1': 'https://huggingface.co/albert-base-v1/resolve/main/spiece.model',
        'albert-large-v1': 'https://huggingface.co/albert-large-v1/resolve/main/spiece.model',
        'albert-xlarge-v1': 'https://huggingface.co/albert-xlarge-v1/resolve/main/spiece.model',
        'albert-xxlarge-v1': 'https://huggingface.co/albert-xxlarge-v1/resolve/main/spiece.model',
        'albert-base-v2': 'https://huggingface.co/albert-base-v2/resolve/main/spiece.model',
        'albert-large-v2': 'https://huggingface.co/albert-large-v2/resolve/main/spiece.model',
        'albert-xlarge-v2': 'https://huggingface.co/albert-xlarge-v2/resolve/main/spiece.model',
        'albert-xxlarge-v2': 'https://huggingface.co/albert-xxlarge-v2/resolve/main/spiece.model',
    },
    'tokenizer_file': {
        'albert-base-v1': 'https://huggingface.co/albert-base-v1/resolve/main/tokenizer.json',
        'albert-large-v1': 'https://huggingface.co/albert-large-v1/resolve/main/tokenizer.json',
        'albert-xlarge-v1': 'https://huggingface.co/albert-xlarge-v1/resolve/main/tokenizer.json',
        'albert-xxlarge-v1': 'https://huggingface.co/albert-xxlarge-v1/resolve/main/tokenizer.json',
        'albert-base-v2': 'https://huggingface.co/albert-base-v2/resolve/main/tokenizer.json',
        'albert-large-v2': 'https://huggingface.co/albert-large-v2/resolve/main/tokenizer.json',
        'albert-xlarge-v2': 'https://huggingface.co/albert-xlarge-v2/resolve/main/tokenizer.json',
        'albert-xxlarge-v2': 'https://huggingface.co/albert-xxlarge-v2/resolve/main/tokenizer.json',
    },
}

a				={
    'albert-base-v1': 512,
    'albert-large-v1': 512,
    'albert-xlarge-v1': 512,
    'albert-xxlarge-v1': 512,
    'albert-base-v2': 512,
    'albert-large-v2': 512,
    'albert-xlarge-v2': 512,
    'albert-xxlarge-v2': 512,
}

a				='▁'






class   __UpperCAmelCase		(      __lowerCAmelCase      ):
				A__ :  Dict    				=			VOCAB_FILES_NAMES
				A__ :  List[Any]    				=			PRETRAINED_VOCAB_FILES_MAP
				A__ :  List[Any]    				=			PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
				A__ :  Union[str, Any]    				=			AlbertTokenizer

				def __init__( self      ,					_lowerCamelCase=None      ,					_lowerCamelCase=None      ,					_lowerCamelCase=True      ,					_lowerCamelCase=True      ,					_lowerCamelCase=False      ,					_lowerCamelCase="[CLS]"      ,					_lowerCamelCase="[SEP]"      ,					_lowerCamelCase="<unk>"      ,					_lowerCamelCase="[SEP]"      ,					_lowerCamelCase="<pad>"      ,					_lowerCamelCase="[CLS]"      ,					_lowerCamelCase="[MASK]"      ,					**_lowerCamelCase      ,					):
										# Mask token behave like a normal word, i.e. include the space before it and
										# is included in the raw text, there should be a match in a non-normalized sentence.
										lowerCamelCase__   =(
										    AddedToken(_lowerCamelCase      ,					lstrip=_lowerCamelCase      ,					rstrip=_lowerCamelCase      ,					normalized=_lowerCamelCase )
										    if isinstance(_lowerCamelCase      ,					_lowerCamelCase )
										    else mask_token
										)

										super().__init__(
										    _lowerCamelCase      ,					tokenizer_file=_lowerCamelCase      ,					do_lower_case=_lowerCamelCase      ,					remove_space=_lowerCamelCase      ,					keep_accents=_lowerCamelCase      ,					bos_token=_lowerCamelCase      ,					eos_token=_lowerCamelCase      ,					unk_token=_lowerCamelCase      ,					sep_token=_lowerCamelCase      ,					pad_token=_lowerCamelCase      ,					cls_token=_lowerCamelCase      ,					mask_token=_lowerCamelCase      ,					**_lowerCamelCase      ,					)

										lowerCamelCase__   =do_lower_case
										lowerCamelCase__   =remove_space
										lowerCamelCase__   =keep_accents
										lowerCamelCase__   =vocab_file
										lowerCamelCase__   =False if not self.vocab_file else True

				def 						_a      ( self      ,					_lowerCamelCase      ,					_lowerCamelCase = None ):
										lowerCamelCase__   =[self.sep_token_id]
										lowerCamelCase__   =[self.cls_token_id]
										if token_ids_a is None:
																return cls + token_ids_a + sep
										return cls + token_ids_a + sep + token_ids_a + sep

				def 						_a      ( self      ,					_lowerCamelCase      ,					_lowerCamelCase = None ):
										lowerCamelCase__   =[self.sep_token_id]
										lowerCamelCase__   =[self.cls_token_id]

										if token_ids_a is None:
																return len(cls + token_ids_a + sep ) * [0]
										return len(cls + token_ids_a + sep ) * [0] + len(token_ids_a + sep ) * [1]






				def 						_a      ( self      ,					_lowerCamelCase      ,					_lowerCamelCase = None ):
										if not self.can_save_slow_tokenizer:
																raise ValueError(
																    "Your fast tokenizer does not have the necessary information to save the vocabulary for a slow "
																    "tokenizer." )

										if not os.path.isdir(_lowerCamelCase ):
																logger.error(F'''Vocabulary path ({save_directory}) should be a directory''' )
																return
										lowerCamelCase__   =os.path.join(
										    _lowerCamelCase      ,					(filename_prefix + "-" if filename_prefix else "") + VOCAB_FILES_NAMES["vocab_file"] )

										if os.path.abspath(self.vocab_file ) != os.path.abspath(_lowerCamelCase ):
																copyfile(self.vocab_file      ,					_lowerCamelCase )

										return (out_vocab_file,)


